document.write( "Question 1176779: 1.The distribution of the number of people in line at a grocery store has a mean of 3 and a variance of 9.
\n" ); document.write( " A sample of the numbers of people in line in 50 stores is taken - Calculate the probability that the sample mean is more than 4. - Calculate the probability the sample mean is less than 2.5. - Calculate the probability that the sample mean differs from the population mean by less than 0.5. \n" ); document.write( "
Algebra.Com's Answer #804249 by ewatrrr(24785)\"\" \"About 
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document.write( "Hi\r\n" );
document.write( "Normal distribution:  mean of 3, a variance of 9  and σ = 3\r\n" );
document.write( "Sample:  n = 50\r\n" );
document.write( "  \"z+=blue+%28x+-+mu%29%2Fblue%28sigma%2Fsqrt%28n%29%29\"  3/sqrt(50) = .4242640687\r\n" );
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document.write( " P( x̄ > 4) = 1 - P( x̄ ≤  4)  0r 1 - P(z ≤ 1/(3/sqrt(50)) = 1-.6306\r\n" );
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document.write( " P( x̄ < 2.5) = P( x̄ ≤ 2.5)  0r P(z ≤ -.5/(3/sqrt(50)) = .4338\r\n" );
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document.write( " P( x̄ < .5) = P( x̄ ≤ .5)  0r P(z ≤ -2.5/(3/sqrt(50)) = .2023\r\n" );
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document.write( "Wish You the Best in your Studies.\r\n" );
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